Ooooohhh.... The wondrous works of the almighty Yukito Kishiro... *Drools at Alita*

Another good series, preceding Battle Angel, but set in the same world, is the series "Ashen Victor". The dark, minimalistic story of the king of crash in the awesome sport of Motorball, Snev. Alita played Motorball at one point, but this guy came before her, and kicked ass, but at the price of his mind and soul.